{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0ab21fefc6f55da02fdb94be4178294b3d9a71d18578abc77e7338756b81f049","created":"2026-10-03T07:18:08Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"88133ea81037460724a17aa708b5b4f05e212e9ea984a971fe23eb520e83d246","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"plasma.collisionless-shocks.electron-injection","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Shocks accelerate particles that bounce back and forth across them many times, but electrons are too small to do this until they are already energetic. How a fraction of thermal electrons is pre-energized is the electron injection problem.","posed_since":"","precise":"Diffusive shock acceleration (DSA, repeated shock crossings by particles scattered by magnetic turbulence) requires electron gyroradii larger than the shock width (of order the ion inertial length). Determine the injection efficiency and the electron-to-proton ratio $K_{\\mathrm{ep}}$ at equal energy as functions of Alfvenic Mach number $M_A$, sonic Mach number and shock obliquity $\\theta_{Bn}$ at realistic $m_i/m_e$. An answer is $K_{\\mathrm{ep}}(M_A, \\theta_{Bn})$ from converged kinetic simulations, compared with $K_{\\mathrm{ep}} \\sim 1e-3\\ \\text{to}\\ 1e-2$ inferred in supernova remnants.","problem_ref":null,"references":"","settled_by":"Long-duration particle-in-cell simulations at realistic mass ratio, confirmed by in-situ spacecraft data at heliospheric shocks.","status_note":"2025 kinetic simulations proposed a shock-speed-dependent injection threshold for electrons (arXiv:2506.09134).","title":"Electron injection into diffusive shock 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